physics simple harmonic motion problem?

Question

A 2.8 kg block is between two horizontal springs. Neither spring is strained when the block is at the position labeled x = 0 m in the drawing. The left spring constant is k(left) = 470 and the right spring constant is k(right) = 660. The block is then displaced a distance of 0.057 m from the position where x = 0 m and is released from rest.

(a) What is the speed of the block when it passes back through the x = 0 m position?

(b) Determine the angular frequency of this system.

http://www.webassign.net/CJ/p10-22.gif

Answer 1

(a) let v be the speed of the block when it passes back through the x = 0 m position where the total energy is the kinetic energy 1/2 m v^2. That should be equal the total elastic potential energy 1/2 k1 x^2 + 1/2 k2 x^2 = 1/2 (k1 + k2) x^2
so m v^2 = (k1 + k2) x^2
v = x * sqrt[(k1 + k2)/m]

angular frequency of this system = sqrt[(k1 + k2)/m]